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WOMAN: Exercise 7.

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Find the constant term
in the expansion

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of (x + 1 divided by x squared)
all to the power of 6.

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The general term in the expansion
of (a + b) all to the power of n

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is n choose r
times a to the power of n minus r

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times b to the power of r,
where r is between 0 and n inclusive.

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So in this particular expansion

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the general term will be 6 choose r
times x to the power of 6 minus r

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times 1 divided by x squared
all to the power of r,

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where r is between
0 and 6 inclusive.

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So considering this general term,
we need to work out

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which value of r is going
to give us the constant term,

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and we acknowledge that
the constant term will occur

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when the 'x's in the general
term cancel out.

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And in this case that's going
to happen when r is equal to 2,

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which will give 6 choose 2
x to the power of 4

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and 1 divided by x squared
all squared,

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which, when we tidy that up a little,

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gives us 15x to the power of 4
times 1 over x to the power of 4.

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So x to the power of 4
is going to cancel out,

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leaving us with
a constant term of 15.